Description of the Related Art
The present invention relates to a method and an arrangement for generating an output signal the frequency of which is twice the frequency of an input signal.
In a known method of frequency doubling, a cyclic input signal is multiplied by the input signal which has been delayed by a quarter of the cycle period. A typical implementation of such a method is, for example, the Gilbert multiplier. An arrangement of this kind is known from EP 1 187 310 A2, for example.
A particular disadvantage which known arrangements of this kind suffer from is that they are made up of a relatively large number of components and have a large number of nodes to which an a.c. signal is applied. The disadvantage this has, particularly at high frequencies, is that the capacitive load becomes very high and integration becomes difficult.
This disadvantage is overcome in accordance with the invention by a method having the features given in claim 1 and by an arrangement having the features given in claim 9.
In accordance with the present invention, an input signal and a delayed signal are rectified and the difference between the rectified signals is determined. The delayed signal may be generated as a function of the input signal in this case, in which case the delayed signal is delayed relative to the input signal by a quarter of the latter""s cycle period but is of the same frequency. Often however, the delayed signal will already exist, as will be the case for example when use is made of an oscillator which produces two signals which are shifted by a quarter of the cycle period and of which one can then used as the input signal and the other as the delayed signal. The present invention is based on the fact that a rectified trigonometrical function given by the following formula can be described as a series expansion of a trigonometrical function of twice the frequency, with the higher terms being severely damped in this case.                                           abs            ⁡                          (                              sin                ⁡                                  (                                      2                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                    f                    ⁢                                          xe2x80x83                                        ⁢                    t                                    )                                            )                                =                                    2              π                        -                                          4                π                            ⁢                                                ∑                                      i                    =                    1                                    ∞                                ⁢                                  xe2x80x83                                ⁢                                                      cos                    ⁡                                          (                                              2                        ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  f                          ·                          2                                                ⁢                                                  xe2x80x83                                                ⁢                                                  i                          ·                                                      xe2x80x83                                                    ⁢                          t                                                                    )                                                                                                  4                      ⁢                                              i                        2                                                              -                    1                                                                                      ⁢                  xe2x80x83                                                  abs          ⁡                      (                          cos              ⁡                              (                                  2                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                  f                  ⁢                                      xe2x80x83                                    ⁢                  t                                )                                      )                          =                              2            π                    -                                    4              π                        ⁢                                          ∑                                  i                  =                  1                                ∞                            ⁢                                                                    (                                          -                      1                                        )                                    i                                ⁢                                  xe2x80x83                                ⁢                                                      cos                    ⁡                                          (                                              2                        ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  f                          ·                          2                                                ⁢                                                  xe2x80x83                                                ⁢                                                  i                          ·                                                      xe2x80x83                                                    ⁢                          t                                                                    )                                                                                                  4                      ⁢                                              i                        2                                                              -                    1                                                                                          
Because the sine function is delayed by a quarter of the cycle period relative to the cosine function, the input signal and the delayed signal can be associated with a cosine function and a sine function respectively. Once the difference between the rectified input signal and the rectified delayed signal has been formed, what is obtained is the following formula as a series expansion of the output signal.             abs      ⁡              (                  cos          ⁡                      (                          2              ⁢                              xe2x80x83                            ⁢              π              ⁢                              xe2x80x83                            ⁢              f              ⁢                              xe2x80x83                            ⁢              t                        )                          )              -          abs      ⁡              (                  sin          ⁡                      (                          2              ⁢                              xe2x80x83                            ⁢              π              ⁢                              xe2x80x83                            ⁢              f              ⁢                              xe2x80x83                            ⁢              t                        )                          )              =            8      π        ⁢          xe2x80x83        ⁢                  ∑                  i          =          1                ∞            ⁢              xe2x80x83            ⁢                        cos          ⁡                      (                          2              ⁢                              xe2x80x83                            ⁢              π              ⁢                              xe2x80x83                            ⁢                              f                ·                2                            ⁢                                                (                                                            2                      ⁢                                              xe2x80x83                                            ⁢                      i                                        +                    1                                    )                                ·                                  xe2x80x83                                ⁢                t                                      )                                                4            ⁢                                          (                                                      2                    ⁢                    i                                    +                  1                                )                            2                                -          1                    
It can be seen from this formula that a dominant term appears on the right-hand side at twice the input frequency and that the higher-frequency terms are severely damped. Advantageously, it is only uneven multiples of the desired output frequency that appear. This fact is particularly advantageous to enable jitter to be avoided.
This method of frequency doubling is particularly suitable for implementation in a semiconductor chip. For this purpose, use is made of a differential input signal and a differential delayed signal which each comprise a positive and a negative component signal. The component signals of the input signal and the component signals of the delayed signal are, for their part, once again cyclic signals but they have different signs, which means that the positive half-waves of one component signal are in phase with the negative half-waves of the other component signal. By means of the component signals of both the input signal and the delayed signal, signals are applied to circuit-switching elements, such as transistors for example, with each current-switching element being so controlled by a component signal that the positive and negative half-waves of the component signal are converted at different gains into component currents flowing through the current-switching elements. Provision may in particular be made for the corresponding current-switching element to block at a positive or negative half-wave of one component signal. This may, for example, be achieved by controlling a transistor by means of a voltage, in which case the negative half-waves of the voltage cause a negative voltage to be applied to the control input of the transistor, which may be the base or gate, for example.
The two component currents which flow through the current-switching elements to which the component signals of either the input signal or the delayed signal are applied are added and thus form a summed signal which corresponds to the rectified input signal or the rectified delayed signal. For rectification of this kind to work, it is essential for the positive and negative half-waves of the component signals not to be converted into currents in the same way. As soon as either the positive or the negative half-waves of the component signals produce a current which is less than proportional, due in particular to blocking of the current switching element, what is produced by the summing of two component currents is rectification either of the input signal or of the delayed signal, and this in itself gives twice the frequency.
The two summed signals are current signals which generate a voltage signal across a resistor or reactor, i.e. an impedance, which means that the output signal can be generated at little cost or complication by means of two resistors or reactors to each of which one summed signal is applied. For this, it is enough for one end of each of the two resistors or reactors to be held at a constant voltage to enable the output signal to be picked off from the other ends of respective resistors or reactors. The resistors or reactors may be ohmic resistors or inductive reactors or a combination of ohmic resistors and inductive reactors. What may also be used as resistors or reactors are semiconductor structures, such as field-effect transistors for example, which are operated in particular in the linear range.
In an advantageous embodiment, the output signal may be filtered to remove unwanted signal components. What may be used in this case is in a particular a low-pass filter or a band-pass filter, in which case the filtering and the nature of the filtering will be suited to the intended field of application of the invention.